What causes a chemical reaction to happen?

There are two aspects to this question: thermodynamics and kinetics.
It is a fundamental law that the entropy of the universe must increase for a process to be feasible. This implies that the Gibbs Free Energy Change ΔG must be negative for a reaction to be feasible. It is given by ΔG= ΔH-TΔS where ΔH and ΔS are the enthalpy and entropy changes of the system and T is the temperature. [Derivation beyond A Level but could do in tutorial if tutee was interested.]
However, for a reaction to be noticeable, it must have a fairly high rate. The rate depends on the temperature, the stability of transition states and intermediates, the strength of the reacting bonds, and the geometries of the molecules, among other factors. The rate constant for a reaction is given by the Arrhenius equation.